X-ray Photon Correlation Spectroscopy (XPCS)and Coherent X-ray Diffraction Imaging (CXDI)

Examples from ESRF and Perspectives for X-ray Lasers

Anders MadsenEuropean Synchrotron Radiation Facility

Grenoble, France

Outline:

• XPCS history

• Current capabilities and forthcoming upgrades at ESRF

• CXDI at ESRF

• XPCS at synchrotrons vs. X-ray lasers

• Concluding remarks

XPCS history

First ESRF paper in 1995 (Troika, Fe3Al)First SAXS paper 1995 (X25 NSLS, Au colloids in glycerol)

Dedicated XPCS beamlines: Troika ID10A/C (ESRF)8-ID (APS)

Total output: 40-50 papers/year

Keywords: physics oriented, specialist’s technique

Competitors/colleagues arrive(d): Diamond Light Source, Swiss Light Source, Petra III, NSLS-2,…….

What about LCLS and X-FEL ???

Troika (ID10): One of the first operational beamlines at ESRF (1992)

Troika I: Open undulator beamline (general purpose, UM since 1994) Later, the Troika I branch specialized in XPCS

ID10B (Troika II): Independent side branch for GID & XR (since 1998)

Troika III: End-station (since 2001). Specialized in coherent SAXS/XPCSRecent developments of CXDI

Top view

Source

2 U27 (27mm period, 11mm min. gap) and 1 U35 undulator. 4.8m in total

Coherent intensityBrilliance

Set n.1: Troika I@8keV Set n.2: Troika III@8keV Set n.3: Troika III@7.2keV

Gain factor: ≈8 Gain factor: ≈10

FWHM: 20µm FWHM: 21µm FWHM: 22µm

Unit 1: 2 CRLs with 200µm radius (Troika I, ~1:3@8keV);Unit 2: 2 CRLs with 300µm radius (Troika III, ~1:1@8keV);Unit 3: 1 CRL with 300µm radius (Troika III, ~1:1@7.2keV);

CRLs in white beam at ID10A

B. Lengeler et al

Medipix detector: 256 x 256 pixels, 55 µm pixel size Photon counting, Upper and lower energy threshold, 30Hz readout

(C. Ponchut, ESRF)

Maxipix-2 detector

>1kHz full-frame readout, 65k pixels, 55µm pixel size, photon counting

Wish: Faster, more pixels, hardware correlator via FPGA (smart detector)

now with 2 chips,soon with 4…..

Maxipix-2 detector

Maxipix-2 detector

SAXS pattern, 1kHz

Current max. speed: 1200 frames/s

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675 shifts/year requested on average

385 shifts/year provided on average

Over-subscription: 1.75

Main request from soft-matter (SC)and hard-condensed matter (HE+HS)

requested/available shifts Distribution on committees

Request for XPCS

Low-frequency elastic behavior of a supercooled liquid, Europhys. Lett. 83, 36001 (2008)

Nano particles in a glass forming solvent, Phys. Rev. Lett. 100, 055702 (2008)

Magnetic colloids: J. Appl. Cryst. 40, 250 (2007), J. Phys. Cond. Mat. 18, S2697 (2006)

X-ray fluorescence correlation spectroscopy: J. Appl. Cryst. 40, 283 (2007)

Charge stab. colloids J. Chem. Phys. 126, 104905 (2007), Phys. Rev. Lett. 96, 138303 (2006)

SrTiO3 displacive transition: Phys. Rev. Lett. 98, 105501 (2007)

Nano-particles on the surface of thin polymer films: Phys. Rev. Lett. 98, 047801 (2007)

Dynamical heterogeneity in colloidal gels: Phys. Rev. E 76, 051404 (2007)

Transient gelation: Phys. Rev. E 76, 010401(R) (2007)

Partially wetting thin liquid films: Phys. Rev. Lett. 99, 096104 (2007)

Bulk fluctuations in a lamellar phase: Phys. Rev. E 74, 031706 (2006)

Coarsening dyn. in alloys: Phys. Rev. B 73, 180101 (2006), Phys. Rev. E 74, 041107 (2006)

Ordering Kinetics in a Cu-Pd Alloy: Phys. Rev. B 72, 144201 (2005)

Grazing incidence XPCS: J. Sync. Rad. 12, 786 (2005)

XPCS Microrheology: J. Phys.: Condens. Matter 17, L279 (2005)

coherentX-rays

Medipix-II detectorLow T SAXS chamber

From diffusive motion to cooperative ballistic behavior near Tg

KWW: 1))(2exp()()2( +Γ−= γβ ttg

Fundamental changes at ~1.2Tg

Nanoparticles in 1,2-propanediol

The goal is to achieve faster times and larger Q to investigate the dynamic properties of e.g. supercooled liquids (α, β relaxations) on “molecular” lengthscales

(necessitates: higher Brilliance, larger and faster 2d detector)

SNR ∝ B τ1/2 S(q)

Capillary waves on highly viscous liquids: Γ = 2γ/η Q

What happens as η!∞ i.e. at the transition from asupercooled liquid to a glass ?

What happens with the shear response as the liquid solidifies?

RHEOLOGY (modulus=stress/strain)

Liquid: deforms cont. under stressSolid: equilibrium deformation under stress

Liquid: stress relaxes under a constant strainSolid: constant stress level under constant strain

2D detector

beamstop

αi < αc

deflectingmirror

pinholeaperture

slits

sample(liquid or solid)

monochromaticsynchrotron beam

Intensity fluctuations of the speckle pattern reflect the dynamics of the sample

Specklepattern

2),(

),()0,(),(

tqI

tqIqItqg =XPCS ! Intensity auto-correlation function

Grazing incidence XPCS

10

0

0)(2)(1

2)( −

∞

++

+=Γ

Gqqqq γ

ηγ

CW dynamics on poly-propylene glycol (PPG)

G(ω)=iωη(ω)+E

Γ!E/η for q!0

Elastic behavior of supercooled liquids is an extremely controversialtopic in the literature and non-invasive experimental methods are missing

Viscoelasticity of poly-propylene glycol (PPG)

η~exp(A/(T-T0)) VTF law

E~exp(A/(T-T0)) VTF law

Y. Chushkin, C. Caronna, and A. Madsen, Europhys. Lett. 83, 36001 (2008)

Towards faster XPCS at larger Q and on weaker signalsPURPLE BOOK CDR: XPCS-CXS

1) Faster and better 2d detectors for the µs regime:Pixel detectors APD arraysSmart detectors

2) Higher coherent flux:Coherence preservationNo undulator sharingNo semi-transparent diamond beam-splitter

3) Reduce beam damage:XPCS at higher energy ?Work further away from the sourceOptimized sample environments

Large pixels necessitate longer sample-detector distance i.e. larger hutches

Separate ID10A and B

Optimized beam tailoring (size, bandwidth) in the range 7-20keV. Larger source-sample distance

and larger hutches

Idea: separation of the Troika beamlines

Coherent scattering and XPCS moves to ID22

Advantages: higher brilliance, beamsplitter diamond out, large dev. potential

Possible long term upgrades of XPCS at ESRF

ID10

ID22

With increasing data-rates on-line calculation of correlationfunctions becomes challenging but very important

The multi-tau algorithm (K. Schätzel) can be “parallelized” to runin multiple processor (cluster) environments

Ensemble averaging (non-ergodic samples); equilibrium(one-time) or non-equilibrium (two-time) correlation functions

Speed can be increased by use of FPGAs (intelligent detector)

Crucial point for a state-of-the-art XPCS beamline

On-line data reduction/data analysis

On-line data reduction/data analysis

Ttp

Ttp

tpp

tQItQI

tQItQIQg

≤≤−≤≤

+=

τφτφ

φτ

τ),(),(

),(),(),(

0

)2(

φφ

φ

),(),(

),(),(),,(

21

2121 tQItQI

tQItQIttQG

pp

pp=

Higher order correlation functions

Beam damage

Huge problem for soft condensed matter, increasing problem with higher flux

Possible ways to minimize beam damage:! Right choice of X-ray energy! 2D detection with shutter in front of sample)! Intelligent sample environment (flowing liquid samples)! Working in a low-flux mode (large sample-source distance)

But in some cases the problem persists, and may create effects thatmimic e.g. aging in soft glasses and gels

Sample environments

droplet generator

J.-B. Salmon, CNRS-Rhodia, Bordeaux

flow cell

A. Fluerasu et al, J. Sync. Rad. 15, 378 (2008)

flow

no flow

Coherent X-ray Diffraction Imaging

Phase retrievaland FFT-1

Phase retrievaland FFT-1

SEM image

SEM image

Logo physics

E. Lima, F. Glassmeier, F. Zontone, and A. Madsen

Towards bio-CXDI at Troika

on-axis microscope

mirror

on-axis microscope

lens

Cryo-jet(100K)

cells ona vitreousmembrane

X-rays

Cells: ~2µm

Towards bio-CXDI at Troika

Deinococcus Radioduransspeckle pattern (hydrated, unstained)

E. Lima, L. Wiegart, P. Pernot, F. Zontone, M. Mattenet, E. Papillon, J. Timmins, and A. Madsen

8 keV

HIO/ER+shrink wrap

Reconstructionnot shown…

Towards bio-CXDI at Troika

3D bio-CXDI, in progress…………..

-70o … 70o rotation

array ofDR cells

hologram

P CCD

Troika IIIbeam

FT(hologram)

Hard X-ray Holographic Diffraction Imaging

Running the phase retrieval algorithm with the FT result as supportone can refine the structure and reconstruct the structure AND the reference dots

Resolution ~25nm (close to diffraction limit)

Advantage: Very fast convergence of algorithm due to good starting conditions

Hard X-ray Holographic Diffraction Imaging

L.-M. Stadler, C. Gutt, T. Autenrieth, O. Leupold, S. Rehbein, Y. Chushkin, and G. Grübel, PRL 100, 245503 (2008)

CXDI with nano-beam

Beam size 100x100nm

ID13 – ESRFE=15.25 keV

C. Schroer et al, PRL 101, 090801 (2008)

10 min exposureReconstruction with5nm resolution

Aucolloids

Is XPCS big enough for both X-ray Lasers and Synchrotrons?

Yes, because• we address different length and timescales

Work at APS and ESRF paved the road but

• The scientific case for XPCS needs to be further developed and broadened

• The technique must be improved

• We can’t continue being an ‘experts only’ techniquei.e. the community needs to grow

Brilliance considerations…

ESRF:

Ic = B λ2/4=1.5e20*1e6*(1.5e-7mm)2 /4*0.14=1.2e11ph/s

Ac=(λ*D/rh,v)2=265µm (v) x 7µm (h)

1pulse (73 fs) of LCLS contains 1.1e12 ph120 pulses/s =1.3e14 ph/s

1012 ph/pulse LCLS

time

8.3msInter image correlations: <C(IN,IM)>

Scheme will probably work for some samples. It is recommended to foresee high quality (no scattering, coherence preserving) beam attenuators

What could be done with 1e12ph on 10ms timescalescompared to today (109 ph/10ms @ ESRF) i.e. factor 103

LCLS

factor 103

SAXS: study dynamics (ms-s) of ultra dilute weakly scattering systems. Higher order correlations. Improve existing XPCS capabilities in slow dynamics (buried interfaces, solid surfaces, polymers, proteins, binary fluids, glasses, ….). High energy?

dσ/dΩ ∝ n V2 (∆ρ)2

Further out in Q, but Q-n power laws eat 103 very fast

10nm particle diffusing in H2O, can LCLS study that?

D0=kBT/6πηR, Γ=120Hz ! Qmax=2.4x10-3 nm-1 (USAXS)

factor 103

WAXS: critical fluctuations, order-disorder transitions, amorphous materials (metallic glasses), charge or spin dynamics in correlated materials, polarization effects, out of equilibrium dynamics, dynamical scaling,…..

All these experiments are today flux limited, i.e. large potential gain with LCLS

Issues for inter-image correlation spectroscopy: beam damage, stability, longitudinal coherence, normalization,…

Inter-image correlation spectroscopy can be seen as thenatural extrapolation of XPCS to AC X-ray laser sources

1010 photons in split pulse LCLS

Split and delay of the pulsesIntra image correlations: <C(I,∆t)>N

Contrast analysis of double exposures will give access to ps-ns timescales

Drawback: efficiency of split delay ~1%Averaging difficult, individual images must have statistical significance

What could be done with 1e10ph on 1ns timescales?

∆t=1ns

∆t=50ps

∆t=500ps

∆t=100ps

LCLS

10nm particle diffusing in H2O, can LCLS detect that?

1ns ! 109 Hz ! Q=7nm-1. Is there enough intensity?

Example (1% vol. Au particles, 100micron pixel size, 1m distance)

Γ=1ns, Q=7nm-1

2e-3 ph/pixel/image

Γ=109Hz, Q=2.1nm-1

2 ph/pixel/image

1nm particle diffusing in H2O, can LCLS detect that?

1ns ! 109 Hz ! Q=2.1nm-1. Is there enough intensity?

Example (1% vol. Au particles, 100micron pixel size, 1m distance)

Within reach !(many pixels in detector)

Detector must be noise free,2d, 100% eff., 120Hz rep. rate

Speckle size, sample-detectordistance (need for spatial filter?)

Important that split-delay line has high throughput

Dynamics of functional biomolecules all length scales and timescales matter

a cell can quasi-instantaneously switch on or off its permeability for a protein over the whole surface; that can only be understood as a collective dynamical phenomenon Movie: Theoretical and Computational Biophysics

group, University of Illinois

Nano/picosecond dynamics on nanoscale in condensed matter• Molecular excitations (vibrational, rotational)• Brillouin scattering (phonons)• Chemistry• Magneto dynamics• Polymers and bio-materials

Concluding remarks:

XPCS at LCLS and 3rd generation machines will to a large extent be complementary0.01-1000 µs will be difficult to cover with the laser

1012 ph/pulse seems a lot, but not enough to saturate the detector at the relevant Qs

Conceptual difference between inter- and intra image correlation schemes

Both schemes provide new possibilities and challenges

Pump-probe XPCS experiments will become feasible (maybe all experiments will inevitably be pump-probe)

Possible that CXDI and XPCS techniques could merge in the future

Very demanding detector development ahead…….